What’s that all about the contrasts

Example dataset

Create a random dataset with criteria y, predictors x1 and x2 and gender.

Al variables are correlated.

n <- 10000
gender <- rep(0:1, each = n/2)
y <- sample(0:10, n, replace = TRUE) + gender * sample(0:10, n, replace = TRUE)
x1 <- y + sample(0:10, n, replace = TRUE) + gender * sample(0:10, n, replace = TRUE)
x2 <- y + x1 + sample(0:10, n, replace = TRUE) + gender * sample(0:10, n, replace = TRUE)

dat <- data.frame(y = y, x1 = x1, x2 = x2, gender = gender)

Descriptives

psych::corr.test(dat)

Call:psych::corr.test(x = dat)
Correlation matrix 
          y   x1   x2 gender
y      1.00 0.81 0.87   0.55
x1     0.81 1.00 0.93   0.67
x2     0.87 0.93 1.00   0.72
gender 0.55 0.67 0.72   1.00
Sample Size 
[1] 10000
Probability values (Entries above the diagonal are adjusted for multiple tests.) 
       y x1 x2 gender
y      0  0  0      0
x1     0  0  0      0
x2     0  0  0      0
gender 0  0  0      0

 To see confidence intervals of the correlations, print with the short=FALSE option

psych::describe(dat)

	vars	n	mean	sd	median	trimmed	mad	min	max	range	skew	kurtosis	se
y	1	10000	7.4871	4.572672	7.0	7.27850	4.4478	0	20	20	0.3501775	-0.4129928	0.0457267
x1	2	10000	15.0661	7.392861	14.0	14.76500	7.4130	0	39	39	0.3575956	-0.4521592	0.0739286
x2	3	10000	30.0596	13.752671	28.0	29.50787	14.8260	0	74	74	0.3339310	-0.5830752	0.1375267
gender	4	10000	0.5000	0.500025	0.5	0.50000	0.7413	0	1	1	0.0000000	-2.0002000	0.0050003

Contrasts

#, contrasts = list(gender = contr.treatment(2))

# Gender has values 0 vs. 1 (treatment contrast)
fit1 <- lm(y ~ gender * x1 * x2, data = dat)


# Gender hast -1 vs. 1 (effect contrast)
dat$gender <- car::recode(dat$gender, "0 = -1; 1 = 1")

fit2 <- lm(y ~ gender * x1 * x2, data = dat)

sjPlot::tab_model(fit1, fit2, show.std = TRUE, show.ci = FALSE, col.order = c("est", "se", "std.est", "p"), digits = 4)

	y			y
Predictors	Estimates	std. Beta	p	Estimates	std. Beta	p
(Intercept)	-1.7456	0.0088	<0.001	-2.5621	0.0088	<0.001
gender	-1.6330	-0.1693	<0.001	-0.8165	-0.1693	<0.001
x1	0.0016	-0.0039	0.941	0.0062	-0.0039	0.657
x2	0.3352	1.0002	<0.001	0.3369	1.0002	<0.001
gender × x1	0.0092	-0.0006	0.741	0.0046	-0.0006	0.741
gender × x2	0.0032	-0.0027	0.830	0.0016	-0.0027	0.830
x1 × x2	-0.0001	-0.0064	0.881	-0.0003	-0.0064	0.518
(gender × x1) × x2	-0.0003	-0.0037	0.707	-0.0002	-0.0037	0.707
Observations	10000			10000
R2 / R2 adjusted	0.764 / 0.764			0.764 / 0.764